RU-ALLRUSSIAN 1989 Problem 23

N is the set of positive integers. Does there exist a function f: $\mathrm{N}\to \mathrm{N}$ such that $\mathrm{f(n + 1)} = \mathrm{f}(\mathrm{f(n)}$ ) + f( $\mathrm{f(n + 2)}$ ) for all n.